The Iraqi military said it was striving to avoid civilian casualties but at least 21 non-combatants are reported to have been killed already since the assault began on Monday.

Fallujah has been under siege by Iraqi forces since February and the Norwegian Refugee Council (NRC), an aid group, said it was hearing reports of people starving to death as no food has been able to reach the city.

“They were faced with two impossible choices,” said Becky Bakr Abdulla of the NRC. “If they stay in Fallujah they face possible starvation, if they try to escape they risk being killed getting out.”

Iraqi pro-government forces advance towards the city of Fallujah as part of a major assault to retake the city from Islamic State.Credit:
AFP PHOTO / AHMAD AL-RUBAYEAHMAD AL-RUBAYE

One woman who escaped the city told Ms Abdulla that she had heard of a mother who drowned herself and three children in order to avoid starvation. The report could not be immediately verified.

Meanwhile, Isil was also under attack in Syria as Kurdish troops backed by Arab fighters struck north of the group's "capital" in the city of Raqqa.

The Syria Democratic Forces (SDF) alliance said it had no intention of trying to liberate Raqqa itself but that it hoped to drive jihadist fighters out of several key nearby towns.

"The current battle is only to liberate the area north of Raqqa. Currently there is no preparation to liberate Raqqa, unless as part of a campaign which will come after this campaign has finished," an SDF spokesman said.

Both offensives will add to the battlefield pressure on Isil, which has lost 46 per cent of its territory in Iraq and 16 per cent in Syria, according to the US.

A senior Isil official said in a public address last week that the so-called "caliphate" would continue to function even if it lost its territorial holdings - a message that some experts interpreted as Isil admitting it was likely to lose more ground.

But both the Fallujah and Raqqa offensives also underscore the fragile coalitions of ground forces aligned against Isil.

Fallujah is a mainly Sunni city and the US has urged Iraq's Shia-dominated military and its Iranian-backed militia allies to tread carefully during the attack to avoid stoking Sunni resentments.

A top commander in Iran's Revolutionary Guard, Qassem Soleimani, is believed to playing a major role in the Fallujah attack. Photographs show the Iranian general, who is also coordinating pro-Assad forces in Syria, huddled with Iraqi Shia militia leaders near Fallujah.

Only around 100 families have managed to escape the city since US airstrikes and Iraqi shelling began in earnest, according to the NRC, and civilians have been warned they will be executed if they try to leave.

Those who have made it out are taking refuge in a temporary camp outside the city. "We urge all parties to this conflict to provide safe exits for civilians out of Fallujah," the NRC said.